Speaker
Micha Berkooz
Description
Field theories on anti-de Sitter (AdS) space can be studied by realizing them as low-energy limits of AdS vacua of string/M theory. In an appropriate limit, the field theories decouple from the rest of string/M theory. Since these vacua are dual to conformal field theories, this relates some of the observables of these field theories on anti-de Sitter space to a subsector of the dual conformal field theories. We exemplify this `rigid holography' by studying in detail the six-dimensional ${\cal N}=(2,0)$ $A_{K-1}$ superconformal field theory (SCFT) on $AdS_5\times \mathbb{S}^1$, with equal radii for $AdS_5$ and for $\mathbb{S}^1$. We choose specific boundary conditions preserving sixteen supercharges that arise when this theory is embedded into Type IIB string theory on $AdS_5\times \mathbb{S}^5 / \mathbb{Z}_K$. On $\mathbb{R}^{4,1}\times \mathbb{S}^1$, this six-dimensional theory has a $5(K-1)$-dimensional moduli space, with unbroken five-dimensional $SU(K)$ gauge symmetry at (and only at) the origin. On $AdS_5\times \mathbb{S}^1$, the theory has a $2(K-1)$-dimensional `moduli space' of supersymmetric configurations. We argue that in this case the $SU(K)$ gauge symmetry is unbroken everywhere in the `moduli space' and that this five-dimensional gauge theory is coupled to a four-dimensional theory on the boundary of $AdS_5$ whose coupling constants depend on the `moduli'. This involves non-standard boundary conditions for the gauge fields on $AdS_5$. Near the origin of the `moduli space', the theory on the boundary contains a weakly coupled four-dimensional ${\cal N}=2$ supersymmetric $SU(K)$ gauge theory. We show that this implies large corrections to the metric on the `moduli space'. The embedding in string theory implies that the six-dimensional ${\cal N}=(2,0)$ theory on $AdS_5\times \mathbb{S}^1$ with sources on the boundary is a subsector of the large $N$ limit of various four-dimensional ${\cal N}=2$ quiver SCFTs that remains non-trivial in the large $N$ limit. The same subsector appears universally in many different four-dimensional ${\cal N}=2$ SCFTs. We also discuss a decoupling limit that leads to ${\cal N}=(2,0)$ `little string theories' on $AdS_5\times \mathbb{S}^1$.
